Almagro and Dominguez-lino (Conditionally accepted at Econometrica)
Wharton UPenn
February 5, 2025
Socioeconomic inequality is tightly linked to residential choice.
Important mechanism that amplifies this inequality: Endogenous amenity.
Thus, fully characterizing this nature of endogenous amenity is important in understanding its effect on welfare inquality.
Households’ diverse tastes for different consumption amenities (horizontal differentiation of neighborhood on the demand side).
Fims providing such amenities cater to this heterogeneity (differential supply-side responses to consumer heterogeneity).
A more full picture to help design policies that alleviate urban inequality.
Possibly due to lack of data, model, shock, etc.
Shift-share IV regression to causally estimate the impact of mass tourism on local housing and amenity markets.
Identification: “Shift” (time variation in worldwide demand for STR) - “Share” (neighborhood-level exposure to tourism using spatial distribution of historic monuments)
Build a dynamic model of a city’s rental market that consists of:
Focus on within-city margin but silent on the mechanisms through which specific amenities are provided: Bayer et al. (2007); Guerrieri et al. (2013); Ahlfeldt et al. (2015); Su (2022).
Impose structure on amenity but lack heterogeneity in residents’ preferences over amenities or collapse amenities into a single quality index: Couture et al. (2021); hoelzlein (2020); Miyauchi et al. (2021).
Calder-Wang (2021): Distributional effects of STR industry on NYC rental market.
Allen et al. (2021): The effects of seasonal tourism on prices of goods and amenities borne by residents of Barcelona.
Two level of geographic units: 99 neighborhoods (wijk) in 25 larger districts (gebied).
ACD: Annual neighborhood-level outcomes (ethnic, income, rich set of consumption amenities, city-level tourist inflows).
Set of amenities are narrowed down to six: Restaurants, bars, food stores, non-food stores, nurseries, and “touristic amenities.”
Final sample: Annual panel of location choices and characteristics for 2008-2018 in 22 districts.
Fact 1: Tourists and STR listings have grown dramatically and sprawled across Amsterdam.
Fact 2: Rents have increased more in neighborhoods with more STR entry.
Fact 3: Amenities have tilted towards tourists and away from locals.
Fact 4: The composition of residents has changed heterogeneously across neighborhoods.
Notation: \(J+1\) locations; \(K\) types of locals and tourist type \(T\); \(S\) sectors; Population composition \(M_{jt} \equiv [M_{jt}^1, ... , M_{jt}^K, M_{jt}^T]'\); Amenities \(a_{jt} \equiv [N_{1jt}, ..., N_{sjt}]'\)
Household with Cobb-Douglas (CD) perferences over housing \(H\) and amenities \(C\), CD preferences across amenity sector and CES preferences over varieties within a sector:
\[q_{isjt} = \sum_k q_{isjt}^k M_{jt}^k, \quad \text{where} \, \, q_{isjt}^k = \frac{\alpha_s^k \phi^k \omega_t^k}{p_{isjt}}\left( \frac{p_{isjt}}{P_{sjt}}\right)^{1-\sigma_s}\]
\[(p_{sjt} - c_{sjt}) q_{sjt} = \underbrace{F_{sjt}(N_{jt})}_{\text{Fixed cost per period}}, \quad \text{where} \, \, N_{jt} = \sum_s N_{sjt}.\]
\[N_{sjt} = \frac{1}{\sigma_s F_{sjt}} \sum_k \alpha_s^k \phi^k \omega_t^k M_{jt}^k, \quad a_{jt}=A(M_{jt})\]
Total housing stock (measured in units of floor space) \(H_{jt}\) is assumed to be inelastic in the short-rn and follows an exogenously determined path over time. Justfication
A continuum of absentee landlords make a binary choice between renting in the long-term market (LT) or in the short-term market (ST).
\[\max\{ \alpha \cdot \overbrace{\gamma_{jt}}^{\text{LT income}} + \varepsilon_{LT}, \, \, \alpha \cdot \underbrace{p_{jt}}_{\text{ST income}} - \overbrace{\kappa_{jt}}^{\text{operating cost}} + \varepsilon_{ST} \},\]
\[H_{jt}^{LT,S} (\gamma_{jt}, p_{jt}) = \frac{\exp(\alpha \gamma_{jt})}{\exp (\alpha \gamma_{jt}) + \exp(\alpha p_{jt} - \kappa_{jt})} H_{jt},\]
\[H_{jt}^{ST,S} (\gamma_{jt}, p_{jt}) = H_{jt} - H_{jt}^{LT,S} (\gamma_{jt}, p_{jt}).\]
Invidual state variables: Location \(j_{it-1}\) and Tenure \(\tau_{jt-1}\).
Aggregate state variables: Rent \(\gamma_t\), Amenities \(a_t\), Exogenous location attributes \(b_t\), and unobservable factors \(\zeta_t\).
\[V^k (x_{it}, \varepsilon_{it}, \underbrace{\omega_{t}}_{\text{aggregate state}}) = \max_{j \in \{ 0, 1, ..., J \}} u^k (j, x_{jt}, \omega_{t}) + \varepsilon_{ijt} + \beta \mathbb{E} \left[ V^k(x_{it+1}, \varepsilon_{it+1}, \omega_{t+1}) \mid j, x_{it}, \varepsilon_{it} \right].\]
If we assume \(\varepsilon_{ijt} \sim \text{T1EV}\), we can also get probability a type \(k\) household chooses \(j\), conditional on state \(x_{it}\): \(\mathbb{P}_{t}^k (j \mid x_{it})\).
We can also denote \(\pi_t^k (j, \tau)\) as type \(k\)’s joint probability of living in location \(j\) with tenure \(\tau\) at the end of period \(t\).
Then, type \(k\) population count for location \(j\) is: \(M_{jt}^k (\gamma_t, a_t) = \sum_\tau \pi_t^k (j, \tau) M_t^k \quad \forall k \in \{ 1, ...,K \}\).
\(\exists\) an exogenous number of tourists \(M_t^T\) arriving into the city and choosing to stay in a short-term rental or a hotel.
Payoff for tourists in STR: \(u_{jt}^{ST} = \delta_j^{ST} + \delta_{t}^{ST} + \delta_p^{ST} \log p_{jt} + \delta_a^{ST} \log a_{jt} + \zeta_{jt}^{ST}.\)
(number of tourists staying in STR): \(M_{jt}^{ST} (p_t, a_t) = \frac{\exp (u_{jt}^{ST})}{\sum_{j' = 0}^J \exp (u_{j't}^{ST})} \cdot M_t^T\).
Population composition, rents, STR prices, and amenities are endogenously and jointly determined in stationary equilibrium.
Definition (Stationary equilibrium) - Brief version
In stationary equilibrium,
the long-term rental market clears for every location,
the short-term rental market clears for every location,
the amenities market clears.
Re-arranging equation in the model and taking logs: \(\log N_{sjt} = - \log F_{sjt}(N_{jt}) + \log \left( \sum_k \beta_s^k \phi^k \omega_t^k M_{jt}^k \right)\) Model-eq Identification
Estimation of \(\beta_s^k \equiv \alpha_s^k/\sigma^s\): Parameter that shows how population’s expenditure is allocated to each amenity sector \(s\).
The paper estimate (normalization of the hotel option’s payoff to zero): \(\small \log \mathbb{P}_{jt}^{ST} - \log \mathbb{P}_{t}^H = \delta_j^{ST} + \delta_t^{ST} + \delta_p^{ST} \log p_{jt} + \delta_a^{ST} \log a_{jt} + \zeta_{jt}^{ST}\)
Estimation: log difference between two supply choices
\[\log H_{jt}^{LT,S} - \log H_{jt}^{ST,S} = \alpha (\gamma_{jt} - p_{jt})+ \kappa_j + \kappa_t + \nu_{jt}\] model-eq Identification
Compare it with homogeneous preference specification: Less sorting, higher inequality.
STR tax or a touristic amenities (TA) tax: Monotonic welfare increase for STR tax, but more nuanced for TA tax.
Examine the impact of removing forward-looking behavior (\(\beta = 0\)) and location capital, i.e., the dynamic state-dependent component of moving costs.
Most of the coefficients of the demand estimates become significantly different, hinting the importance of dynamic component in the model.
This paper studies the role of preference heterogeneity over a set of endogenous location amenities in shaping within-city sorting and welfare inequality.
Heterogeneity in the preferences of residents and supply responses of firms are substantial.
Distributional incidence of urban policies depends on heterogeneity on both demand and supply side of the amenities market.
On average, annual growth of housing stock in Amsterdam is 1.2%, similar to the 0.9% value for San Francisco, one of the least housing-elastic cities in the US.
Also, the assumption of inelastic housing supply is broadly in line with other studies of housing supply in the Netherlands (Vermeulen and Rouwendal, 2007).
Parameterize \(F_{sjt}(N_{jt}) = \Lambda_j \Lambda_t \cdot \underbrace{R(N_{jt})}_{\text{annual rental price of commercial real estate}} \cdot \Omega_{sjt}\)
Assume \(R(N_{jt}) = N_{jt}^\eta\), where \(\eta\) is inverse supply elasticity of real-estate (calibrated).
Identification issue: Amenity supply shock is correlated with \(N_{sjt}\) and \(M_{jt}^k\). We need amenity demand shifters as IV.
The paper constructs an instrument that shift population composition: \(Z_{jt}^k = \omega_t^k \cdot\underbrace{S_{jt}^{\gamma(k)}}_{\text{housing stock by tenancy status}}\).
OLS estimation leads to bias due to simultaneity bias from regressing quantities on prices.
Use shift-share predicted tourist demand as IV.